Write a critical note on limitations of statistics.
Write a critical note on limitations of statistics.
Or
“The science of statistics is more useful servant but only of great value to those who understand its proper use”. Comment on the above statement and discuss the limitations of statistics.
Ans.
Continuous precaution and vigilence are necessary to be free from misuse of statistics. Wallis and Robert have said to this extent, “external vigilence is the price of freedom from serious statistical blunders.” As such, neither data nor statistical science are responsible for distrust in statistics. Persons having no knowledge about the limitations of statistics and who are selfish and prejudiced are responsible for misuse of statistic and which create suspicion in the minds of common people. Prof King bas rightly said, “The science of statistics, then, is a most useful servant but only of great value to those who understands its proper use.”
Limitations of Statistics
Although statistics is universally applicable, yet it is not free from limitations. These limitations must be taken into consideration otherwise the results arrived at will be misleading. In the words of Newsholme. “It (statistics) must be regarded as an instrument of research of great value but having severe limitations which are not possible to overcome and as such they need our careful attention.”
The following are the limitations of statistics :
(1) Statistics studies only numerical data and not qualitative phenomena :
Only quantitative facts are studied with the help of statistics, e.g., prices, production, age, height, etc. Some qualitative facts like intelligence, friendship, poverty, honesty, etc. cannot be studied directly through statistics though some of such facts can be subject to a study in an indirect form. For example, to study the intelligence of students, marks obtained in an intelligent test may be taken as a base and to study the problem of poverty, persons may be classified according to their incomes. But whenever the qualitative facts are measured indirectly, the accuracy and correctness of which is always subject to doubt and suspicion.
(2) Statistics Study the Aggregates and not the individuals : Statistics deals with the aggregates of facts and not the characteristics of individual item in a series. Although the average income of citizens in a town is obtained by dividing total incomes of citizens of that town but their number, yet it does not tell about the financial position of individuals. It throws light on average income of the group, not the individuals. For example, who is poor or below poverty line, who is rich, who is a beggar etc. Similarly if during a year rainfall in four towns of a district was 20,90,70 and 100 cms respectively, the average rainfall in the district would be [(20 + 90 +70+ 100) ÷ 4] 70 cms. It will not speak of individual towns that town number one was dry on account of very less rainfall which will go unattended because of the average rainfall being 70 cms. Thus, it is not necessary that the conclusions of a group shall apply to individuals.
(3) Statistical Methods are not the only Methods to Study: According to Croxton and Cowdon, “it must not be assumed that the statistical method is the only method to use in research, neither should this method be considered the best attack for every problem.”
For the solution of a problem statistical method is one of the methods and it is not the only approach for decision making. The results derived by these methods should be assumed as appropriate only after testing the same through other methods like deduction method etc. Even then statistical methods are more appropriate for the study and solution of any problem. Dr. Bowley has rightly said, “It is necessary, however, to its solution as accurate measurements are for the construction of a Building.”
(4) Statistical conclusions can be misleading without References: The conclusions or interpretations of the results of statistical analysis should not be made without referring to the context. For example, the average profits of three trading enterprises may be the same, it would be fallacious to state that all enterprises are uniform in their respective progress. If the entire data of all these enterprises are kept in view, the conclusions may be that one is progressing every year, the other may be decaying gradually while the third one may be statistic.
(5) Statistical Conclusions are True on an average and during long period: The inferences drawn on the basis of statistical studies are not perfectly true as in case of laws propounded under natural sciences. For instance, under chemistry the law is that a man will die immediately after his taking potassium cyanide. The law would hold good whether one gram or 10 grams of it is used. Similarly, under physics according to law of gravity every article which is dropped from above will always be attracted towards earth. But statistical laws though based on the theory of probability, are not true to such an extent. For example, the probability of a head or a tail is equal on tossing of a coin, but if the coin is tossed twice it cannot be definitely said that once it would be head and once the tail. Here if the coin is tossed a large number of times, say 5000 it can be fairly said that the results would almost be approximate to equality. Thus, statistics depicts approximate tendencies only.
(6) The data should be Homogeneous and Uniform : Before making comparison, it must be confirmed that the data are homogeneous and uniform. Different and hitrogeneous types of data cannot be compared. For example, the growth of population of a country cannot be compared with increase in production of wheat or rice etc.
(7) Statistics can be used only by Experts : Only such persons can collect, analyse and interpret suitably the statistical data who possess adequate knowledge of statistical methods. Inexpert and untrained persons cannot draw correct inferences from the collected data. Their results or conclusions would be wrong and fallacious.
In the words of Yule and Kendall, “Statistical methods are the most dangerous tools in the hands of the inexperts. The use of statistical tools by inexperienced and untrained persons might lead to very fallacious conclusions. One of the main shortcomings of statistics is that they do not bear on their face the label of their quality and as such can be moulded and manipulated in a manner one likes. As King says “Statistics are like clay of which one can make a god or devil as one pleases.” The requirement of experience and skill for judicious use of statistical methods restricts their use to experts.
